A variable dimension solution approach for the general spatial price equilibrium problem
Mathematical Programming: Series A and B
Mathematical Programming: Series A and B
A new continuation method for complementarity problems with uniform P-functions
Mathematical Programming: Series A and B
Newton's method for the nonlinear complementarity problem: a B-differentiable equation problem
Mathematical Programming: Series A and B
Mathematical Programming: Series A and B
Mathematical Programming: Series A and B
A nonsmooth version of Newton's method
Mathematical Programming: Series A and B
Convergence analysis of some algorithms for solving nonsmooth equations
Mathematics of Operations Research
NE/SQP: a robust algorithm for the nonlinear complementarity problem
Mathematical Programming: Series A and B
A class of smoothing functions for nonlinear and mixed complementarity problems
Computational Optimization and Applications
A semismooth equation approach to the solution of nonlinear complementarity problems
Mathematical Programming: Series A and B
A Theoretical and Numerical Comparison of Some Semismooth Algorithms for Complementarity Problems
Computational Optimization and Applications
A New Merit Function For Nonlinear Complementarity Problems And A Related Algorithm
SIAM Journal on Optimization
Journal of Optimization Theory and Applications
A Smoothing Newton Method for General Nonlinear Complementarity Problems
Computational Optimization and Applications
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The complementarity problem is theoretically and practically useful, and has been used to study and formulate various equilibrium problems arising in economics and engineerings. Recently, for solving complementarity problems, various equivalent equation formulations have been proposed and seem attractive. However, such formulations have the difficulty that the equation arising from complementarity problems is typically nonsmooth. In this paper, we propose a new smoothing Newton method for nonsmooth equations. In our method, we use an approximation function that is smooth when the approximation parameter is positive, and which coincides with original nonsmooth function when the parameter takes zero. Then, we apply Newton's method for the equation that is equivalent to the original nonsmooth equation and that includes an approximation parameter as a variable. The proposed method has the advantage that it has only to deal with a smooth function at any iteration and that it never requires a procedure to decrease an approximation parameter. We show that the sequence generated by the proposed method is globally convergent to a solution, and that, under semismooth assumption, its convergence rate is superlinear. Moreover, we apply the method to nonlinear complementarity problems. Numerical results show that the proposed method is practically efficient.